Derivative synthesis of musical instrument tones by means of nonlinear transfer function device



3,530,225 was Sept. 22, 1970 E. GSCHWANDTNER DERIVATIVE SY BY MEANS O NTHESIS OF MUSICAL INSTRUMENT 'IO F NONLINEAR TRANSFER FUNCTION DEVICE 3 SheetsSheet l 7 Filed Sept. 6, 1966.

Sept. E1. GSCHWANDTNER 3,530,

DERIVATIVE SYNTHESIS OF MUSICAL INSTRUMENT TUNES BY MEANS OF NONLINEAR TRANSFER FUNCTION DEVICE Filed p 6, 1966 :5 Sheets-Sheet J52 W 1 6 J74 J66 I jg 154 J55 K] I & J56

J70 g J60 J A u J 3 J6K w wwmyzw p 1970 E. GSCHWANDTNER 3,530,225

DERIVATIVE SYNTHESIS OF MUSICAL INSTRUMENT TONES BY MEANS OF NONLINEAR TRANSFER FUNCTION DEVICE Filed Sept. 6, 1966 3 Sheets-Sheet 5 g4 96 J00 36 45 J06 J02 56" 84 1 ascuumq '\J 1mmw/ 2Z2, wag/5% United States Patent 3,530,225 DERIVATIVE SYNTHESIS OF MUSICAL INSTRU- MENT TONES BY MEANS OF NONLINEAR TRANSFER FUNCTION DEVICE Eric Gschwandtner, Rexdale, Ontario, Canada, asslgnor to The Wurlitzer Company, Chicago, 11]., a corporation of Ohio Filed Sept. 6, 1966, Ser. No. 577,203 Int. Cl. Gltlh 1/02 U.S. Cl. 841.13 16 Claims ABSTRACT OF THE DISCLOSURE A musical instrument tone (e.g., clarinet) device wherein a nonlinear transfer function of voltage input versus voltage output is provided by a combination of a plurality of active devices and a plurality of quiescent devices. The nonlinear transfer function comprises a plurality of straight line segments and may be symmetric about a predetermined operating point (or quieseent point). The quiescent point is fixed and the curve is ad ustable to determine the desired output wave form. The circuitry includes a pair of back-to-back Zener diodes and a pair of transistors.

This invention relates to the art of electronic musical instruments, and more particularly relates to derivative synthesis of musical instrument tones by means of a nonlinear transfer function.

Most conventional musical instruments produce oscillations of rather complex wave form. However, the wave form typically varies in complexity in accordance with the amplitude of Wave produced, or the amount of energy fed into the instrument. Typically, when an instrument is played at a rather low level, its output tends to be of rather simple wave form. Indeed, if excitedat a sufficiently low level, most conventional musical instruments tend to approach a sine wave output. As the instrument is excited with more energy, generally producing a louder tone, the wave form becomes more complex, and may become increasingly more complex with still greater excitation. As a typical example, a clarinet blown very softly produces a rather pure tone. When blown a little harder, it produces a moderately complex tone, and when it is blown still harder, it produces a still further complex tone. For the most part, the wave comprises a fundamental and a series of overtones. However, particularly at the start of reed vibration, there are some inharmonic partials, typically of a transient nature. As will be appreciated, this is a normal manner of excitation of a clarinet, and of most other wind instruments. The amount of air at first blown is a minimum, and the amount increases up to a normal maximum, and then tapers off at the end. That is to say, typically there is not an instantaneous beginning and end.

As will be appreciated, percussive instruments such as pianos, drums, cymbals, etc. produce a different type of tone in which the intensity is substantially at a peak at the start and decreases thereafter. Typically, the sound wave is most complex at the start, and becomes progressively simpler as the tone decays.

Efforts heretofore have been made to simulate conventional instruments electronically. In many respects, the desired wave forms have been approached fairly closely, but there has been in almost every instance a lack of the changing wave form complexity at the start and the end of a tone which is necessary for a really desirable simulation of the natural tones. Some highly complex efforts have been made to add harmonics sequentially by additive synthesis, using computef-type circuits for control,

but these have been of commercially impractical complexity.

Accordingly, it is an object of this invention to provide electrical means for simulating natural musical tones, or for producing novel musical tones, including changes of wave form complexity with changes in intensity.

A further object of the present invention is to provide electronic means for musical tone generation in which an oscillator need produce only a simple or sine wave, with the sine wave being electrically converted to a changing complex wave form.

More particularly, it is an object of the present invention to provide an electronic musical instrument generating a simple sine wave which is converted or derivatively synthesized into a complex wave form changing with intensity of the sine Wave oscillations by a nonlinear transfer function.

Every amplifying device has a transfer function, whether it be an electron tube or a solid state device. Generally speaking, it is desired to keep the transfer function as nearly a straight line as possible, so as to produce an output wave as close as possible in form to the input wave. Some transfer functions depart from straight line, generally in a rather simple fashion, and are tolerated, rather than desired.

A particular transfer function is used in the present invention to provide a desired wave form output of changing complexity as will appear hereinafter. As exemplary of the principles of the present invention, a clarinet tone has been chosen which, as is well known, has a series of odd harmonics with no substantial even harmonics.

Various objects and advantages of the present invention in addition to those before enumerated will be apparent from the following description when taken in connection with the accompanying drawings wherein:

FIG. 1 is a schematic view of a nonlinear transfer function and of the input and output waves transferred thereby;

FIG. 2 is a graphical representation of the fundamental and certain harmonics at various positions in time;

FIG. 3 is a schematic or block diagram for the production of one note in an electronic musical instrument;

FIG. 4 is a schematic wiring diagram of a suitable transfer function circuit;

' FIG. 5 is a graphic representation of the transfer function as produced thereby; and

FIG. 6 is a schematic diagram similar to FIG. 3 with added features.

' Turning now in greater particularity to the drawings, and first to FIG. 1, there will be seen at the upper left hand corner thereof a transfer function 10. This transfer function includes a central straight portion 12 at substantially a 45 angle passing through a neutral point 14 and symmetrical thereabout. As will be appreciated, the straight line portion 12, leading from a lower left limit 16 to an upper right limit 18 is quite conventional in nature. However, from the point 18 the transfer function extends as a straight line horizontally to the right at 20, while concomitantly there is a straight line portion 22 extending horizontally to the left from the point 16. The horizontal straight line portion 20 terminates at a point 24, and the transfer function then extends steeply up to the right at 26 through a point 28. Similarly, there is a left limit point 30 to the straight line portion 22, and the transfer function then extends steeply down to the left at 32, parallel to the portion 26, through a point 34.

Immediately below the transfer function there is shown an input wave having an envelope 36. The input wave, designated generally by the numeral 38, is plotted about a vertical axis 40 extending through the neutral point 14. The wave is a sine wave, and starts at the point labeled 42 at zero amplitude, increasing in amplitude (measured on the horizontal axis) with increasing time (vertically down along the axis 40). The sine wave builds up in amplitude from point 42 to another point in time labeled at 44, the space between being labeled as an attack period. From point 44 on, as indicated by the arrow 46, the sine wave is of constant amplitude, labeled sustain. It will be understood that the wave envelope 36 is provided with a decay period, and this will be discussed further with regard to FIG. 3.

Also in FIG. 1 there is indicated an output wave 48 plotted on horizontal axis 50 through the neutral point 14, the vertical axis in tis measure representing amplitude, and the horizontal axis representing time. The output wave presents a complex envelope which will be taken up immediately hereinafter.

When the input wave first starts out at relatively low amplitude, it is transferred to the output solely by he initial straight line portion 12 of the transfer function, thereby producing a sine Wave beginning at 54 to the output wave, the corresponding envelope section 56 being very similar to that of the input wave. However, when the amplitude of the input wave 38 is such as to reach points 16 and 18 on the transfer function there is for the moment no further linear function, due to the horizontal portions 20, 22 of the transfer function, thereby causing the output wave to be clipped or flattened at 58 producing very nearly a square wave. Accordingly, the envelope in this vicinity flattens off at 60.

When the amplitude of the input wave is such as to reach the transfer function points 24 and 30, there is again a linear reproduction or amplification, producing a pip or spike 62 centrally of the fiat tops 58 of the output wave. The flat tops always remain at constant amplitude, but the pips or spikes increase somewhat in amplitude up to the points 28 and 30 of the transfer function, at which locations the input wave reaches its maximum intensity. Thus, upon reaching point 64 on the horizontal time axis of the output wave, corresponding time-wise to the point 44 of the vertical time axis of the input wave, the output wave has stabilized. This ends the attack por tion, as labeled on the curve, and it will be seen that the envelope again produces a convex curve portion 66 from the flat portion 60 up to the level or limit portion 68 during the sustain part of the output curve. As will be understood, when the input wave subsequently decays, the output wave again changes its form.

As will be appreciated, the various complex portions of the output curve are susceptible to a Fourier analysis, and this is represented in FIG. 2. In FIG. 2, there is shown a graph of amplitude versus time for the fundamental waveform at 70. Amplitude is on the vertical axis, and time on the horizontal axis. Time periods are indicated with correspondence to the horizontal time axis at the upper right portion of FIG. 1, and the output wave is considered to start at point t and it will be seen that a more or less convex wave form is produced from time t to time t the period during which the initial linear portion of the transfer function is used. During the next time period, from I to t the fundamental wave increases only slightly in amplitude, and a further nonlinear increase is produced from t to 23 this being the portion of the attack period corresponding to the wave impressed on the transfer function including portions 26 and 32.

Immediately below the fundamental there is reproduced a third harmonic 72, and it will be seen that the third harmonic has no amplitude whatsoever from time t to time t and then increases from 1 to t and decreases slightly from time t to i The fifth harmonic is plotted immediately therebelow at 74, and it will be seen that it likewise has no amplitude from time t to time 11, increases from time t to t and then increases further from t to i mostly immediately after t The seventh harmonic has no amplitude from time t to time and then increases in amplitude from time t to time t Additional odd harmonics could be plotted in generally the same manner, but are not necessary for illustrative purposes. It will be noted that there are no even harmonics, and it will be understood that during the sustain periods beyond t all of the fundamental and various harmonics remain of constant amplitude until a decay period is reached. Initial inharmonic partials have been omitted from the present illustrative example.

A representation of a circuit for one note of an electronic musical instrument utilizing the principles set forth above will be seen in FIG. 3. As will be understood, additional duplicative circuits or structure will be provided for each note. To start with, there is a 13+ supply line or bus 78 connected through a resistor 80 to the movable element of a keyswitch 82. This movable element is engageable with a fixed contact 84, shunted to ground by a capacitor 86, and connected through a line 88 to the oscillator 90. The voltage appearing on the line 88 is indicated at 92, having a convex portion 94 at the start, and a concave portion 96 at the end respectively corresponding to the charging and decay time of capacitor 86. The oscillator is of a type generating a sine wave, and either starts operation upon application of B+ potential thereto, or is constantly operating with the output gated by the B+ potential. The output of the oscillator is connected to a line 98, and the output wave 38 is the same as previously discussed. The envelope 36 has an attack period 100, as previously discussed, and a decay period 102 mentioned, but not heretofore illustrated. As will be seen, the envelope is substantially a symmetrical replica of the DC. voltage appearing on the line 88.

The line 98 is connected to the transfer function 10, and the output wave thereof as indicated at 48 appears on line 104, the envelope 52 being as heretofore shown and described, with the addition of the decay period 106. This is applied to a formant filter 108, and this in turn is connected to an output, which will be understood typically as comprising an amplifier and loud speaker system or equivalent.

As noted, the foregoing circuit is for one note only, the oscillator having a frequency corresponding to the note in question. Similar duplicate circuitry will be provided for each note. However, it will be understood that variations are possible, such as a tunable oscillator with a plurality of key switches connected thereto, and suitable for controlling the frequency in accordance with which of the key switches is closed.

A circuit for producing a nonlinear transfer function 10 is shown in FIG. 4. The circuit includes an input leading back-to-back Zener diodes 112 paralleled by a resistor 114 and connected in common therewith to a junction point 116. The junction point is shunted by back-to-back Zener diodes 118 to the top end of a potentiometer resistor 120, the lower end thereof being grounded, as shown. The potentiometer resistor has a sliding tap 122 thereon, and the connection of this tap to subsequent circuit elements will be set forth hereinafter.

The junction point 116 is also connected through a coupling capacitor 124 to a junction point 126. The junction point 126 forms the center of a voltage divider comprising grounded resistor 128 and a resistor 130 leading to a B+ supply line or bus 132. The junction point 126 is further connected to the base 134 of an N-P-N transistor 136. The emitter 138 of the transistor is connected to a grounded resistor 140, while the collector 142 is connected to a junction point 144. The junction point 144 is connected through a resistor 146 to the B+ supply line 132, and also is connected to a line 148.

The line 148 is connected through a coupling capacitor 150 to an output line 152. The collector 154 of an N-P-N transistor 156 also is connected to the line 148, and the emitter 158 of this transistor is connected to a grounded resistor 160. The base 162 is connected to a junction point 164 on a voltage divider comprising resistor 166 leading to the B+ supply line 132 and a grounded resistor 168, there being a junction point 170 at the top of the resistor 168. This junction point is connected through a coupling capacitor 172 to the potentiometer tap 122.

The sine wave input is indicated at position 110 by the numeral 38, as used heretofore. The Wave shape at junction point 127 is indicated at 174, the wave shape at point 122, the potentiometer tap, being indicated at 176 as a series of alternate pips, with an output wave shape being indicated at 48. As will be observed, the height of the pips on the wave shape 48 is variable within a range starting at zero, and this is produced by the setting of the potentiometer tap 122. As will be appreciated, at very low level input, both Zener diode pairs 112 and 118 will have a high impedance. The effect of the resistor 114 will therefore be at a maximum, and the voltage divider, comprising the Zener diodes 112 and parallel resistor 114, in series with Zener diodes 118 and potentiometer resistor 120 will produce a substantially sine wave at point 116. At higher input amplitudes, the Zener diodes 112 and 118 will become progressively more conductive. The resistor 114 is on the order of ten times the resistance of the potentiometer resistor 120, in one typical example the resistor 114 being 5600 ohms and the potentiometer resistor 120 being 500 ohms. Thus, the Zener diodes 118 begin to conduct before the Zener diodes 112, flattening off the top of the wave, the subsequent conduction of the Zener diodes 112 providing pips on the top of the flattened wave, thereby producing the wave form 174. Until such time as the Zener diodes 118 conduct, there will be no wave on the tap 122 corresponding to the input wave. However, whenever the Zener diodes 118 conduct, a portion of the input wave will be produced, thereby producing the wave shape 176 comprising a series of alternating pips or spikes. As will be apparent, if the tap 122 is set at the bottom of the potentiometer resistor 120, the spikes will be of zero amplitude, and conversely setting the tap at the top of the potentiometer resistor will provide a maximum amplitude for the pips or spikes. These are amplified "by the transistor 156 and associated circuitry, and added to the amplified wave shape 174 at the line 148, whereby the output wave can have greater or lesser height pips as indicated at 48 in FIG. 4.\.

In FIG. 5 the actual transfer function is plotted, as opposed as to idealized transfer function of FIG. 1. Similar numerals are used to identify similar portions of the transfer functions, and it will be seen that the transfer function is the same as that heretofore described, but having the corners somewhat rounded, and also having the portions 26 and 32 adjustable from respectively the point 28 to 28' and 34 to 34, depending on the setting of the tap 122, as just discussed. It will be understood that this is a continuous variation, and not a step wise function.

It will now be seen that there is provided an electronic musical instrument having a simple sine wave oscillator with the oscillation thereof applied to a nonlinear transfer function of voltage input versus voltage output to produce an output tone of varying complexity, the harmonic structure depending on the amplitude on the wave initially generated. The specific example is in connection with a clarinet tone, but it will be understood that other nonlinear transfer functions are within the contemplation of this invention for producing different output waves.

Although the invention has been described with a sine wave input, it will be understood that other input waveforms could be used. The output wave-form will then depend on the complexity of the input wave, bearing in mind that it can be resolved to a complex arrangement of simple waves.

Furthermore, although in the specific example of the invention the oscillator has been referred to as either turned on by the application of B+ potential or as gated thereby, in a broad sense the oscillator can be considered as amplitude modulated by a control signal, specifically B+ as herein described. It is to be understood that the format filter is used in addition to the transfer function because of the constant frequency effect of the format filter (characteristic of a conventional or mechanical musical instrument) as contrasted with the Wave shaping of the transfer function which is independent of frequency. I.e., the format filter always passes the same band or group of frequencies, thus producing a different wave shaping for different frequencies, while the transfer function always produces the same wave shaping, regardless of frequency which may be stated otherwise as spectrum variation independent of frequency.

Various embellishments can be added to the foregoing disclosure, leading to performance that cannot be obtained with common or mechanical musical instruments. Reference therefore should be made to FIG. 6, which is identical with FIG. 3, but with added features. Extra contacts 82a and 82b are added to the key switch and are ganged for operation therewith, respectively being engageable with fixed contacts 84a and 84b. These switch contacts can be rendered effective or ineffective in accordance with known techniques commonly used in the electronic organ art.

A vibrato generator 178 is shown as connected between the B+ line 78 and the resistor, whereby to vary the amplitude modulating (envelope control) potential applied to the oscillator 90, hence to produce a vibrato effect as an optional extra feature.

There is also shown a vibrato generator 178a connected to the B+ line 78 and through a resistor 80a to the switch contact 82a. The contact 84a is connected over a line 88a, having a shunt capacitor 86a, to the oscillator, whereby to produce a vibrato by known techniques.

Perhaps more importantly, the formant filter also can be changed dynamically such as in a cyclic manner, to vary the distinguishing characteristics of the instrument. To this, end, a generator 178k is connected to the B+ line and through a resistor 80b to switch contact 82b. Switch contact 84b is connected by means of a line 88b, shunted by capacitor 86b, to the formant filter 108, and thus to cause a cyclic variation of the formant filter. Rather than cyclic, the formant variation could be in a particular direction each time a key is depressed. Obviously, all of the generators or oscillators 178, 178a and 1781) could be made variable in speed over a substantial range. Circuits are known for dynamic variation of a formant filter, see for example Hearne US. Pat. 3,- 358,069. Reference should be made to formant filter 234, capacitor 296, diode 290 and associated elements.

It is perhaps worthy of re-emphasis that the principles of this invention apply equally well to percussive type instruments such as pianos, drums, etc. in which the amplitude is greatest at or very close to the start and then decays, in contrast to the specific disclosure wherein the amplitude builds up from a minimum at the start.

The specific example of the invention as herein shown and described is for illustrative purposes only. Various changes in structure will no doubt occur to those skilled in the art, and will be understood as forming a part of the present invention insofar as they fall within the spirit and scope of the appended claims.

I claim:

1. An electronic musical instrument comprising means providing a source of electric voltage oscillations corresponding to musical tones, means for controlling the amplitude of electric voltage oscillations provided by said source including manually controllable switch means,

output means, and means interconnecting said source and said output means and including means providing a nonlinear transfer function of voltage input versus voltage output, and said transfer function including a plurality of line segments and said transfer function providing means comprising a plurality of means for respectively determining the characteristics of said line segments, the electric voltage oscillations having a fixed quiescent point on the nonlinear transfer function.

2. An electronic musical instrument as set forth in claim 1 wherein the amplitude controlling means includes means for producing a controlled increase in amplitude upon operation of said switch means in a first direction to provide an attack period.

3. An electronic musical instrument as set forth in claim 1 wherein the amplitude controllnig means includes means for producing a controlled decrease in amplitude upon operation of said switch means in a second direction to provide a decay period.

4. An electronic musical instrument as set forth in claim 1 wherein the amplitude controlling means includes means for producing a controlled increase in amplitude upon operation of said switch means in one direction to provide an attack period and for producing a controlled decrease in amplitude upon operation of said switch means in a second direction to provide a decay period.

5. An electronic musical instrument as set forth in claim 1 wherein said transfer function is symmetrical about a neutral point.

6. An electronic musical instrument as set forth in claim 5 wherein said transfer function comprises a plurality of line segments symmetrical in pairs about said neutral point.

'7. An electronic musical instrument as set forth in claim 6 wherein at least some of said line segments are substantially straight.

8. An electronic musical instrument as set forth in claim 1 wherein said transfer function means transfers oscillations of small amplitude substantially without change in waveform and transfers oscillations of greater amplitude with a predetermined change in waveform.

9. An electronic musical instrument as set forth in claim 1 wherein said transfer function means comprises an interconnected combination of active and passive elements, there being a plurality of active elements.

10. An electronic musical instrument as set forth in claim 6 wherein said transfer function comprises a central substantially linear portion of predetermined slope, additional line portions of substantially zero slope, and further line portions having a slope.

11. An electronic musical instrument as set forth in claim 1 and wherein said transfer function providing means includes means for varying said transfer function. While maintaining said quiescent point.

12. An electronic musical instrument comprising means providing a source of electric voltage oscillations corresponding to musical tones, modulating means connected to said oscillation providing means for modulating said oscillations, nonlinear voltage input versus Voltage output means having a fiXed quiescent or operating point interconnected with said oscillation providing means and said modulating means for producing a spectrum variation independent of frequency, said transfer function including a plurality of line segments and said transfer function providing means comprising a plurality of means for respectively determining the characteristics of said line segments, and formant filter means connected to said nonlinear means.

13. An electronic musical instrument as set forth in claim 12 and further including means for dynamically varying said formant filter.

14. An electronic musical instrument as set forth in claim 13 wherein the means for varying the formant filter includes means for cyclically varying the filter.

15. An electronic musical instrument comprising means providing a source of electric voltage oscillations corresponding to musical tones, means for controlling the amplitude of electric voltage oscillations provided by said source including manually controllable switch means, output means, and means interconnecting said source and said output means and including means providing a nonlinear transfer function of voltage input versus voltage output, said transfer function including a plurality of line segments and said transfer function providing means comprising a plurality of means for respectively determining the characteristics of said line segments, said means providing a nonlinear transfer function comprising a plurality of active devices.

16. An electronic musical instrument as set forth in claim 1 wherein the line segments comprise substantially straight line segments.

References Cited UNITED STATES PATENTS -Re. 6,533 3/1969 Cookerly et al. 841.16 2,036,892 4/1936 Smiley 84l.01 X 2,514,490 7/1950 Hanert 841.0l 2,931,877 4/ 1960 Henley.

3,213,181 10/1965 Snoddy et al. 841.19 2,959,693 11/1960 Meyer 84l.26 X 3,229,020 1/1966 Jenny 841.l3 3,388,257 6/1968 Ten Eyck 841.25 X 2,506,723 5/1950 Larsen 84l.l9 3,333,041 7/1967 Munch et al. 841.l1 3,358,069 12/1967 Hearne 841.03

WARREN E. RAY, Primary Examiner US. Cl. X.R. 

